Permutations and Combinations Answers

A trial jury of 6 people will be chosen from among 18 candidates. How many juries are possible?

Of the 10 contestants in a televised quiz competition, 2 were eliminated during this week’s show, and 2 more will be eliminated during next week’s show. How many groups of 6 remaining contestants are possible a week from now? Assume that the show airs on the same day every week.

A department store is hiring for the positions of manager, associate manager, and assistant manager. If 15 people have applied for all the positions and are equally qualified for each position, in how many ways can the positions be filled?

A baseball team’s roster consists of 25 players with 13 position players and the rest being pitchers. The team’s batting order for a particular game consists of 9 players. The first 8 places in the batting order are taken by position players. The last place is taken by a pitcher. How many batting orders are possible? Use the formula for permutations to find your answer.

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How many combinations are possible for 13 objects taken 6 at a time?

How many permutations are possible for 11 objects taken 7 at a time?

A raffle is being held to raise money for wildlife conservation efforts. Ten different gift cards are being awarded. If 3,125 people each bought a single raffle ticket, which of the following expressions represents the number of ways the gift cards can be awarded? Assume that each person can win only once.

A magician performing a magic act has asked for 2 volunteers from the audience to help with his routine. If there are 250 people in the audience, which of the following expressions represents the number of possible pairs of volunteers?

A president and vice president will be selected from among 35 members of a board. Should permutations or combinations be used when determining the number of possible ways these offices can be filled?